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What Is the Doppler Effect?

The Doppler effect, or Doppler shift, is the change in wavelength and frequency caused by the movement of an observer relative to the source. One of the most common ways we can experience the Doppler effect in action is in the change of pitch that occurs due to a moving sound source. You’ve probably experienced the Doppler effect when a fire truck or ambulance passes by with its sirens blaring. As the siren passes, the pitch suddenly drops as the vehicle begins to move away from you. How can we visualize the Doppler effect in action?

Propagation of sound waves from a sound source.

The Doppler Effect, Explained

As fans of the popular TV-show, The Big Bang Theory, have heard it described, the Doppler effect is the apparent change in the frequency of a wave caused by relative motion between the source of the wave and the observer. But what exactly does this mean?

One of the easiest ways to visualize the Doppler effect is to imagine a bug gliding across the surface of a puddle. First, let’s picture what the disturbances in the puddle would look like if the bug was stationary, vibrating its legs and producing waves in the puddle. The disturbances would propagate outward from the bug in spherical waves, resembling what is seen in the image above. However, what would happen to these waves if the bug started moving across the water? The water flow around the bug would change so that the waves are closer together in front of the bug, and farther apart behind it. This can be seen in the following animation:

The Doppler effect works in much the same way for sound. When a sound source is stationary, the sound that we hear is the same that is emitted from the sound source. However, when the sound source begins to move, the perceived sound changes. Let’s use the ambulance example again. Not only is the sound that we hear different for an ambulance moving away from us, but the sound reaching our ears is different as the ambulance approaches, when it is parallel to our location, and as it recedes.

In the first case, as the ambulance moves toward us, each successive sound wave is emitted from a closer position than that of the previous wave. Because of this change in position, each sound wave takes less time to reach us than the previous one. The distance between wave crests (the wavelength) is thereby reduced, meaning that the perceived frequency of the wave is increased. The sound is perceived to be of a higher pitch. Conversely, as a sound source moves away, waves are emitted from a source that is farther and farther away, therefore creating an increased wavelength, a decreased perceived frequency, and a lower pitch.

Creating a Doppler Effect Simulation

We can use COMSOL Multiphysics and the Acoustics Module to create a simulation of the Doppler effect to measure the change in frequency for a sound source moving at a certain velocity. In our simulation, let’s assume that the air surrounding the sound source (the ambulance in this case) is moving with a velocity of V = 50 m/s in the negative z-direction. We’ll also assume that the observer of the sound is standing 1 m from the ambulance as it passes by. In the figure below, we can see the change in sound pressure level as the ambulance approaches and passes an observer:

A Doppler effect simulation where the distance of the ambulance from the observer is represented on the x-axis.
The solid line represents the pressure perceived by the observer of an approaching ambulance. The dashed line
shows the pressure as the ambulance recedes.

From this plot, we can see how the amplitude of the wave (or pressure) drops off at a faster rate when the ambulance is moving away from an observer compared to when it is approaching. The change in the amplitude of the wave depicts how the siren’s sound becomes quieter as the ambulance moves away. The rate at which the sound level decreases as the ambulance recedes is much faster than the rate at which the sound becomes louder as the ambulance approaches, as can be seen in the graph. We can also visualize the sound pressure level around the sound source:

Sound pressure level around the sound source represented by colors and contour lines. You can see how the
outermost contour runs from well inside the physical domain to the PML, showing that the sound is greater
below than above the source.

Other Examples of the Doppler Effect

The Doppler effect can also be seen in many other phenomena. One common example is the Doppler radar, where a radar beam is fired at a moving target. The time it takes for the radar to bounce off the target and return to the transmitter can provide information about a target’s velocity. Another example is in astronomy, where the Doppler effect is used to determine the direction and rate at which a star, planet, or galaxy is moving compared to the Earth. By measuring the change in the color of electromagnetic waves — called redshift or blueshift — an astronomer can determine the celestial bodies’ radial velocity. Other applications that take advantage of the Doppler effect include sonar, medical imaging and blood flow measurement, satellite communication, and many more.